Djokovic had the openings in the first without converting and Murray made him pay by winning the tie-break.
It was role reversal in the second as Murray wasted that triple chance for an early break as Djokovic held on for a tie-break he won, thanks largely to a Murray double-fault at 2-2.
He put his first serve into the net and was shaping up to deliver the second when he noticed a feather dropping on to the court out of the corner of his eye.
Having removed it, he promptly put the second serve long.
"I could have served," he explained. "But it just caught my eye before. I thought it was a good idea to move it. Maybe it wasn't."
It was all Djokovic needed to level the match and the momentum appeared to swing further in his favour when Murray had to call for the trainer.
Murray required a medical time-out at the end of the third set to treat a nasty-looking blister and he went on to lose the next two as Djokovic claimed his third successive Melbourne crown with a 6-7 (2/7) 7-6 (7/3) 6-3 6-2 success.
There was no immediate deterioration in his movement, although there was the definite sense the match was now Djokovic's for the taking.
And the top seed needed no second invitation as he set up three break points for a 5-3 lead.
Two poor forehands saw the first two come and go but Murray could not escape a third as Djokovic claimed the first break of the match before serving it out.
From there there was no way back as Djokovic broke twice more in the fourth to extend his winning run in Melbourne to 21 matches and take revenge for his defeat to Murray in the US Open final in September.
"I knew it was going to be physically demanding," the Serbian said following the three-hour, 40-minute contest. "So I needed to hang in there.
"There were a few turning points in the match. Maybe one of them was the second game of the second set when I was 0-40 against the breeze. He missed a few shots and I managed to get a crucial hold.
"After that I felt mentally a little bit lighter and more confident on the court than I had done in the first hour or so.
"I went for my shots in the third and fourth and came to the net quite often.
"I needed to be the one who dictated the play and I'm really glad that I played my best."